My trackpad stopped working. I can't get a replacement now, so I've been working all day without it. Fortunately that was not a problem as I barely use it with VIM, ChromeVim, QuickSilver etc. Now I need to change some things on OSX System Preferences and I don't know how to. Is there a mouseless way to interact with it?
If you are comfortable with the command line your best option is the defaults command. For an example of what you can get look here:
That is a good starting point to do your own research. If there is something specific you want to change, you should post a new question.
You may also consider AppleScript which is able to do UI scripting.
For example I used the following AppleScript recently to change my mouse settings (enabling/disabling natural scrolling on Mavericks) :
tell application "System Preferences" reveal pane "com.apple.preference.mouse" end tell tell application "System Events" to tell process "System Preferences" tell checkbox 1 of window 1 click end tell end tell